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A010878
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a(n) = n mod 9.
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19
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0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Periodic with period of length 9. The digital root of n (A010888) is a very similar sequence.
The rightmost digit in the base-9 representation of n. Also, the equivalent value of the two rightmost digits in the base-3 representation of n. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 11 2007
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).
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FORMULA
| Complex representation: a(n)=(1/9)*(1-r^n)*sum{1<=k<9, k*product{1<=m<9,m<>k, (1-r^(n-m))}} where r=exp(2*pi/9*i) and i=sqrt(-1). Trigonometric representation: a(n)=(256/9)^2*(sin(n*pi/9))^2*sum{1<=k<9, k*product{1<=m<9,m<>k, (sin((n-m)*pi/9))^2}}. G.f.: g(x)=(sum{1<=k<9, k*x^k})/(1-x^9). Also: g(x)=x(8x^9-9x^8+1)/((1-x^9)(1-x)^2). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 31 2007
a(n)=n mod 3+3*(floor(n/3)mod 3)=A010872(n)+3*A010872(A002264(n)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 11 2007
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CROSSREFS
| Partial sums: A130487. Other related sequences A130481, A130482, A130483, A130484, A130485, A130486.
Sequence in context: A037851 A037887 A031087 * A190727 A195832 A004184
Adjacent sequences: A010875 A010876 A010877 * A010879 A010880 A010881
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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